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In this paper, we propose METRO, a generic framework with multi-scale temporal graphs neural networks, which models the dynamic and cross-scale variable correlations simultaneously. By representing the multivariate time series as a series of temporal graphs, both intra- and inter-step correlations can be well preserved via message-passing and node embedding update. To enable information propagation across temporal scales, we design a novel sampling strategy to align specific steps between higher and lower scales and fuse the cross-scale information efficiently. Moreover, we provide a modular interpretation of existing GNN-based time series forecasting works as specific instances under our framework. Extensive experiments conducted on four benchmark datasets demonstrate the effectiveness and efficiency of our approach. METRO has been successfully deployed onto the time series analytics platform of Huawei Cloud, where a one-month online test demonstrated that up to 20% relative improvement over state-of-the-art models w.r.t. RSE can be achieved.<\/jats:p>","DOI":"10.14778\/3489496.3489503","type":"journal-article","created":{"date-parts":[[2022,2,5]],"date-time":"2022-02-05T00:28:36Z","timestamp":1644020916000},"page":"224-236","source":"Crossref","is-referenced-by-count":63,"title":["METRO"],"prefix":"10.14778","volume":"15","author":[{"given":"Yue","family":"Cui","sequence":"first","affiliation":[{"name":"University of Electronic Science and Technology of China, China and The Hong Kong University of Science and Technology, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Zheng","sequence":"additional","affiliation":[{"name":"University of Electronic Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dingshan","family":"Cui","sequence":"additional","affiliation":[{"name":"Huawei Cloud Database Innovation Lab, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiandong","family":"Xie","sequence":"additional","affiliation":[{"name":"Huawei Cloud Database Innovation Lab, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liwei","family":"Deng","sequence":"additional","affiliation":[{"name":"University of Electronic Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feiteng","family":"Huang","sequence":"additional","affiliation":[{"name":"Huawei Cloud Database Innovation Lab, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofang","family":"Zhou","sequence":"additional","affiliation":[{"name":"The Hong Kong University of Science and Technology, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2022,2,4]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Time series analysis: forecasting and control","author":"Box George EP","unstructured":"George EP Box , Gwilym M Jenkins , Gregory C Reinsel , and Greta M Ljung . 2015. 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Neural networks for machine learning lecture 6a overview of mini-batch gradient descent. 14, 8 (2012), 2."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.8.1735"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3357384.3358132"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1080.0292"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-014-0631-0"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-47426-3_25"},{"key":"e_1_2_1_19_1","volume-title":"ICLR'15","author":"Kingma Diederik P","year":"2015","unstructured":"Diederik P Kingma and Jimmy Ba . 2015 . Adam: A method for stochastic optimization . In ICLR'15 . 1395--1402. Diederik P Kingma and Jimmy Ba. 2015. Adam: A method for stochastic optimization. In ICLR'15. 1395--1402."},{"key":"e_1_2_1_20_1","volume-title":"Semi-Supervised Classification with Graph Convolutional Networks. In ICLR'17","author":"Thomas","unstructured":"Thomas N. Kipf and Max Welling. 2017 . Semi-Supervised Classification with Graph Convolutional Networks. In ICLR'17 . Thomas N. Kipf and Max Welling. 2017. Semi-Supervised Classification with Graph Convolutional Networks. In ICLR'17."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3209978.3210006"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00029"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.5555\/1241540.1241551"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3397271.3401092"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3184558.3191526"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/BigData.2018.8622109"},{"key":"e_1_2_1_27_1","volume-title":"A stochastic approximation method. 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PMLR, 6285--6294."},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.5555\/3305890.3306039"},{"key":"e_1_2_1_37_1","volume-title":"International conference on learning representations.","author":"Trivedi Rakshit","year":"2019","unstructured":"Rakshit Trivedi , Mehrdad Farajtabar , Prasenjeet Biswal , and Hongyuan Zha . 2019 . Dyrep: Learning representations over dynamic graphs . In International conference on learning representations. Rakshit Trivedi, Mehrdad Farajtabar, Prasenjeet Biswal, and Hongyuan Zha. 2019. Dyrep: Learning representations over dynamic graphs. In International conference on learning representations."},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.5555\/2998981.2999021"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.5555\/3295222.3295349"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(84)90022-8"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-947X(2003)129:6(664)"},{"key":"e_1_2_1_42_1","volume-title":"Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. In KDD'20","author":"Wu Zonghan","year":"2020","unstructured":"Zonghan Wu , Shirui Pan , Guodong Long , Jing Jiang , Xiaojun Chang , and Chengqi Zhang . 2020 . Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. In KDD'20 . Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, and Chengqi Zhang. 2020. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. 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Multi-variate Time Series Forecasting Based on Causal Inference with Transfer Entropy and Graph Neural Network. arXiv preprint arXiv:2005.01185 (2020)."},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33015668"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.5555\/3157096.3157191"},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.5555\/3172077.3172356"},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/3219819.3220024"},{"key":"e_1_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(01)00702-0"},{"key":"e_1_2_1_52_1","volume-title":"Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. In The Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI","author":"Zhou Haoyi","year":"2021","unstructured":"Haoyi Zhou , Shanghang Zhang , Jieqi Peng , Shuai Zhang , Jianxin Li , Hui Xiong , and Wancai Zhang . 2021 . 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